To find the slope of a line that passes through the ordered pairs $(1, 7)$ and $(2, 12)$, we use the slope formula:

$m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

In this case:

• $(x_1, y_1) = (1, 7)$
• $(x_2, y_2) = (2, 12)$

Substitute these values into the formula:

$m = \frac{{12 - 7}}{{2 - 1}} = \frac{5}{1} = 5$

Thus, the slope of the line is $5$.

The correct answer is 5.

Would you like more details or have any questions?

Here are some related questions:

1. How do you find the slope if given points with negative coordinates?
2. How does the slope formula change if both points have the same $x$-value?
3. What does a slope of $0$ indicate about the line?
4. Can the slope be a fraction? What does that represent geometrically?
5. What happens to the line’s slope if the order of points is reversed?

Tip: When calculating slope, remember to subtract coordinates in the same order for both $y$- and $x$-values to avoid sign errors.